A Phenomenological Study of the Cosmic Ray Variations over the Past 9400 Years, and Their Implications Regarding Solar Activity and the Solar Dynamo

Two 9400-year long ¹⁰Be data records from the Arctic and Antarctic and a ¹⁴C record of equal length were used to investigate the periodicities in the cosmic radiation incident on Earth throughout the past 9400 years. Fifteen significant periodicities between 40 and 2320 years are observed in the ¹⁰Be and ¹⁴C records, there being close agreement between the periodicities in each record. We found that the periodic variations in the galactic cosmic radiation are the primary cause for periods <?250 years, with minor contributions of terrestrial origin possible >?250 years. The spectral line for the Gleissberg (87-year) periodicity is narrow, indicating a stability of ≈?0.5 %. The 9400-year record contains 26 Grand Minima (GM) similar to the Maunder Minimum, most of which occurred as sequences of 2?–?7 GM with intervals of 800?–?1200 years in between, in which there were no GM. The intervals between the GM sequences are characterised by high values of the modulation function. Periodicities <?150 years are observed in both the GM intervals and the intervals in between. The longer-period variations such as the de Vries (208-year) cycle have high amplitudes during the GM sequences and are undetectable in between. There are three harmonically related pairs of periodicities (65 and 130 years), (75 and 150 years), and (104 and 208 years). The long periodicities at 350, 510, and 708 years closely approximate 4, 6, and 8 times the Gleissberg period (87 years). The well-established properties of cosmic-ray modulation theory and the known dependence of the heliospheric magnetic field on the solar magnetic fields lead us to speculate that the periodicities evident in the paleo-cosmic-ray record are also present in the solar magnetic fields and in the solar dynamo. The stable, narrow natures of the Gleissberg and other periodicities suggest that there is a strong “frequency control” in the solar dynamo, in strong contrast to the variable nature (8?–?15 years) of the Schwabe (11-year) solar cycle.     

On the Relationship of the 27-day Variations of the Solar Wind Velocity and Galactic Cosmic Ray Intensity in Minimum Epoch of Solar Activity

We study the relationship of the 27-day variations of the galactic cosmic ray intensity with similar variations of the solar wind velocity and the interplanetary magnetic field based on observational data for the Bartels rotation period # 2379 of 23 November 2007 – 19 December 2007. We develop a three-dimensional (3-D) model of the 27-day variation of galactic cosmic ray intensity based on the heliolongitudinally dependent solar wind velocity. A consistent, divergence-free interplanetary magnetic field is derived by solving Maxwell’s equations with a heliolongitudinally dependent 27-day variation of the solar wind velocity reproducing in situ observations. We consider two types of 3-D models of the 27-day variation of galactic cosmic ray intensity, i) with a plane heliospheric neutral sheet, and ii) with the sector structure of the interplanetary magnetic field. The theoretical calculations show that the sector structure does not significantly influence the 27-day variation of galactic cosmic ray intensity, as had been shown before, based on observational data. Furthermore, good agreement is found between the time profiles of the theoretically expected and experimentally obtained first harmonic waves of the 27-day variation of the galactic cosmic ray intensity (with a correlation coefficient of 0.98±0.02). The expected 27-day variation of the galactic cosmic ray intensity is inversely correlated with the modulation parameter ζ (with a correlation coefficient of −0.91±0.05), which is proportional to the product of the solar wind velocity V and the strength of the interplanetary magnetic field B (ζ∼VB). The high anticorrelation between these quantities indicates that the predicted 27-day variation of the galactic cosmic ray intensity mainly is caused by this basic modulation effect.     

Cosmic Ray Intensity Variations in Relation with Solar Flare Index and Sunspot Numbers

From the monthly data of cosmic ray intensity (CRI), sunspot numbers (SSN) and solar flare index (SFI), an attempt has been made to study the relationship between CRI and solar activity (SA) parameters SSN and SFI. The correlation between SA parameters and CRI for different neutron monitoring stations having low, middle and high cut-off rigidity has been investigated. The anti-correlation between SA and CRI is found to exist with some time lag. Based on the method of minimizing correlation coefficient and time-delayed component method, the observed time-lag between SA parameters (SSN and SFI) and CRI has been found to be large for odd solar cycles in comparison to even solar cycles. The results of time-lag analysis between CRI and SSN and between CRI-SFI have also been compared. The findings of correlative study between CRI and SSN are in agreement with earlier results, while the CRI-SFI relationship provides new insights to understand the solar modulation of cosmic rays.     

The 27-Day Cosmic Ray Intensity Variations During Solar Minimum 23/24

We have studied the 27-day variations and their harmonics in Galactic cosmic ray (GCR) intensity, solar wind velocity, and interplanetary magnetic field (IMF) components during the recent prolonged solar minimum 23/24. The time evolution of the quasi-periodicity in these parameters connected with the Sun’s rotation reveals that the synodic period of these variations is ≈?26?–?27 days and is stable. This means that the changes in the solar wind speed and the IMF are related to the Sun’s near-equatorial regions in considering the differential rotation of the Sun. However, the solar wind parameters observed near the Earth’s orbit provide only the conditions in the limited local vicinity of the equatorial region in the heliosphere (within ±?7^° in latitude). We also demonstrate that the observed period of the GCR intensity connected with the Sun’s rotation increased up to ≈?33?–?36 days in 2009. This means that the process that drives the 27-day GCR intensity variations takes place not only in the limited local surroundings of the equatorial region but in the global 3-D space of the heliosphere, covering also higher latitude regions. A relatively long period (≈?34 days) found for 2009 in the GCR intensity gives possible evidence of the onset of cycle 24 due to active regions at higher latitudes and rotating slowly because of the Sun’s differential rotation. We also discuss the effect of differential rotation on the theoretical model of the 27-day GCR intensity variations.     

Cosmic Ray Fluxes in Present and Past Times

The data on primary cosmic ray fluxes at the top of the atmosphere are given for the period since 1937 till the present time. These data have been obtained from the regular cosmic ray flux measurements in the stratosphere and on the ground level. They have been used to find the relationship of cosmic ray fluxes with solar activity (sunspot number). On the basis of the deduced relationship the cosmic ray fluxes in the past have been recovered, as the sunspot number is known since 1500. The link between the smoothed data on Be-10 atom concentrations and cosmic ray fluxes is established which gives a possibility to calculate cosmic ray fluxes in the far past.     

Galactic Cosmic Ray Modulation and the Last Solar Minimum

In this work the galactic cosmic ray modulation in relation to solar activity indices and heliospheric parameters during the years 1996??C?2010 covering solar cycle 23 and the solar minimum between cycles 23 and 24 is studied. A new perspective of this contribution is that cosmic ray data with a rigidity of 10 GV at the top of the atmosphere obtained from many ground-based neutron monitors were used. The proposed empirical relation gave much better results than those in previous works concerning the hysteresis effect. The proposed models obtained from a combination of solar activity indices and heliospheric parameters give a standard deviation <?10?% for all the cases. The correlation coefficient between the cosmic ray variations of 10?GV and the sunspot number reached a value of r=?0.89 with a time lag of 13.6±0.4 months. The best reproduction of the cosmic ray intensity is obtained by taking into account solar and interplanetary indices such as sunspot number, interplanetary magnetic field, CME index, and heliospheric current sheet tilt. The standard deviation between the observed and calculated values is about 7.15?% for all of solar cycle 23; it also works very well during the different phases of the cycle. Moreover, the use of the cosmic ray intensity of 10?GV during the long minimum period between cycles 23 and 24 is of special interest and is discussed in terms of cosmic ray intensity modulation.     

Theoretical and Experimental Studies of the Rigidity Spectrum of the 27-Day Variation of the Galactic Cosmic Ray Intensity in Different Epochs of Solar Activity

Recently Pop (Solar Phys. 276, 351, 2012) identified a Laplace (or double exponential) distribution in the number of days with a given absolute value in the change over a day, in sunspot number, for days on which the sunspot number does change. We show this phenomenological rule has a physical origin attributable to sunspot formation, evolution, and decay, rather than being due to the changes in sunspot number caused by groups rotating onto and off the visible disc. We also demonstrate a simple method to simulate daily sunspot numbers over a solar cycle using the Pop (Solar Phys. 276, 351, 2012) result, together with a model for the cycle variation in the mean sunspot number. The procedure is applied to three recent solar cycles. We check that the simulated sunspot numbers reproduce the observed distribution of daily changes over those cycles.     

Rapid Cosmic Ray Fluctuations: Evidence for Cyclic Behaviour

We study rapid cosmic-ray fluctuations using 5-min resolution data from eight neutron monitors with different cutoff rigidities as well as from the ACE satellite. We define a proxy index of rapid cosmic-ray fluctuations as the mean power of the cosmic-ray power spectrum in the frequency range 10⁻⁴ −1.67 × 10⁻³ Hz (10 min to about 3 h). A dominant 11-year periodicity in the index is found in all neutron monitors. We also report on intermittent, short-term periodicities in the power of rapid cosmic-ray fluctuations. A strong mid-term periodicity of about 1.6 – 1.8 years, possibly related to a recently found similar periodicity in IMF, appears in CR fluctuation power since the 1980s. Another strong periodicity is found at 1 year, which is likely related to the relative position of the Earth in the heliosphere. These results also provide new challenge to test the cosmic-ray modulation theory.     

Study of the Cosmic Ray Diurnal Anisotropy During Different Solar and Magnetic Conditions

The pressure-corrected hourly counting rate data of four neutron monitor stations have been employed to study the variation of cosmic ray diurnal anisotropy for a period of about 50 years (1955–2003). These neutron monitors, at Oulu ( R _c = 0.78 GV), Deep River ( R _c = 1.07 GV), Climax ( R _c = 2.99 GV), and Huancayo ( R _c = 12.91 GV) are well distributed on the earth over different latitudes and their data have been analyzed. The amplitude of the diurnal anisotropy varies with a period of one solar cycle (∼11 years), while the phase varies with a period of two solar cycles (∼22 years). In addition to its variation on year-to-year basis, the average diurnal amplitude and phase has also been calculated by grouping the days for each solar cycle, viz. 19, 20, 21, 22, and 23. As a result of these groupings over solar cycles, no significant change in the diurnal vectors (amplitude as well as phase) from one cycle to other has been observed. Data were analyzed by arranging them into groups on the basis of the polarity of the solar polar magnetic field and consequently on the basis of polarity states of the heliosphere ( A > 0 and A < 0). Difference in time of maximum of diurnal anisotropy (shift to earlier hours) is observed during A < 0 (1970s, 1990s) polarity states as compared to anisotropy observed during A > 0 (1960s, 1980s). This shift in phase of diurnal anisotropy appears to be related to change in preferential entry of cosmic ray particles (via the helioequatorial plane or via solar poles) into the heliosphere due to switch of the heliosphere from one physical/magnetic state to another following the solar polar field reversal.     

Predictions of Galactic Cosmic Ray Intensity Deduced from that of Sunspot Number

A new method is proposed to predict cosmic ray intensity and solar modulation parameters. The method is coupled with the McNish and Lincoln method, which predicts first smoothed sunspot numbers. The error achieved is estimated and compared with the same chain of predictions using two other methods developed for US and Russian space applications. The three methods give satisfactory results when applied, for example, to prediction of the dose received on-board commercial aeroplane flights.     

Harmonics of Low Amplitude Anisotropic Wave Train Events in Cosmic Ray Intensity

The unusually low amplitude anisotropic wave train events (LAWEs) in cosmic ray intensity using the ground based Deep River neutron monitor data has been studied during the period 1991–1994. It has been observed that the amplitude of the diurnal anisotropy for LAWE events significantly remains quite low and statistically constant as compared to the quiet day annual average amplitude for majority of the events. The time of maximum of the diurnal anisotropy of LAWE significantly shifts towards earlier hours as compared to the co-rotational direction and remains in the direction of quiet day annual average anisotropy for majority of the events. On the other hand, the amplitude of the semi/tri-diurnal anisotropy remains statistically the same and high whereas, phase shift towards later hours as compared to the quiet day annual average values for majority of the LAWEs. The diurnal anisotropy vectors are found to shifts towards earlier hours for 50% of the events; whereas they are found to shifts towards later hours for rest of the events (50%) relative to the average vector for the entire period. It is also noted that the amplitude of these vectors are found to increase significantly with the shift of the diurnal anisotropy vectors towards later hours. The high-speed solar wind streams do not play a significant role in causing the LAWE events on short-term basis, however it may be responsible in causing these events on long-term basis (Mishra and Mishra 2007). Occurrence of LAWE is dominant, when the polarity of Bx and Bz remains positive and polarity of By remains negative, which is never been reported earlier. The amplitude of first harmonic shows good anti-correlation and direction of first and third harmonic shows nearly good anti-correlation with solar wind velocity, whereas the direction of second harmonic shows nearly good anti-correlation with interplanetary magnetic field strength.     

Intensity of Cosmic Rays at the Initial Stage of a Solar Flare

The propagation of solar cosmic rays in the interplanetary space is analyzed by solving the Fokker–Planck equation in the small-angle approximation. The particle source is assumed to be instantaneous and point-like. The spatiotemporal distribution of density of energetic particles in the anisotropic phase of a solar cosmic-ray enhancement is examined. Prolonged particle injection into the interplanetary medium is also discussed.     

The Asymptotic Longitudinal Cosmic Ray Intensity Distribution as a Precursor of Forbush Decreases

Identifying the precursors (pre-increases or pre-decreases) of a geomagnetic storm or a Forbush decrease is of great importance since they can forecast and warn of oncoming space weather effects. A wide investigation using 93 events which occurred in the period from 1967 to 2006 with an anisotropy A _xy >1.2% has been conducted. Twenty-seven of the events revealed clear signs of precursors and were classified into three categories. Here we present one of the aforementioned groups, including five Forbush decreases (24 June 1980, 28 October 2000, 17 August 2001, 23 April 2002, and 10 May 2002). Apart from hourly cosmic ray intensity data, provided by the worldwide network of neutron monitor stations, data on solar flares, solar wind speed, geomagnetic indices (Kp and Dst), and interplanetary magnetic field were used for the analysis of the examined cosmic ray intensity decreases. The asymptotic longitudinal cosmic ray distribution diagrams were plotted using the “ring of stations” method. Results reveal a long pre-decrease up to 24 hours before the shock arrival in a narrow longitudinal zone from 90° to 180°.     

Cycling Changes in the Amplitudes of the 27-Day Variation of the Galactic Cosmic Ray Intensity

We study quasi-periodical changes in the amplitudes of the 27-day variation of the galactic cosmic ray (GCR) intensity, and the parameters of solar wind and solar activity. We have recently found quasi-periodicity of three to four Carrington rotation periods (3?–?4 CRP) in the amplitudes of the 27-day variation of the GCR intensity (Gil and Alania in J. Atmos. Solar-Terr. Phys. 73, 294, 2011). A similar recurrence is recognized in parameters of solar activity (sunspot number, solar radio flux) and solar wind (components of the interplanetary magnetic field, solar wind velocity). We believe that the 3?–?4 CRP periodicity, among other periodicities, observed in the amplitudes of the 27-day variation of the GCR intensity is caused by a specific cycling structure of the Sun’s magnetic field, which may originate from the turbulent nature of the solar dynamo.     

Transient Modulation of Cosmic Ray Intensity: Role of Magnetic Clouds and Turbulent Interaction Regions

Two distinct regions of shock-associated magnetic clouds, (i) magnetically turbulent regions formed due to interaction between magnetic cloud and ambient magnetic field i.e. turbulent interaction region (TIR), and magnetically quiet region called magnetic cloud have been considered separately and correlation of interplanetary plasma and field parameters, magnetic field strength (B) and solar wind speed (V), with cosmic ray intensity (I) have been studied during the passage of these two regions. A good correlation between B and I and between V and I has been obtained during the passage of sheath when the magnetic field is high and turbulent, while these correlation have been found to be poor during the passage of magnetic clouds when the field is strong and smooth. Further, there is a positive correlation between enhancement in field strength and its variance in the sheath region. These results strongly support the hypothesis that most Forbush decreases are due to scattering of particles by region of enhanced magnetic turbulence. These results also suggest that it will provide a better insight if not the magnetic field enhancement alone but in addition, the nature of magnetic field enhancement is also considered while correlating the field enhancements with depressions in cosmic rays. This revised version was published online in July 2006 with corrections to the Cover Date.     

Solar Modulation of Cosmic Rays during the Declining and Minimum Phases of Solar Cycle 23: Comparison with Past Three Solar Cycles

We study solar modulation of galactic cosmic rays (GCRs) during the deep solar minimum, including the declining phase, of solar cycle 23 and compare the results of this unusual period with the results obtained during similar phases of the previous solar cycles 20, 21, and 22. These periods consist of two epochs each of negative and positive polarities of the heliospheric magnetic field from the north polar region of the Sun. In addition to cosmic-ray data, we utilize simultaneous solar and interplanetary plasma/field data including the tilt angle of the heliospheric current sheet. We study the relation between simultaneous variations in cosmic ray intensity and solar/interplanetary parameters during the declining and the minimum phases of cycle 23. We compare these relations with those obtained for the same phases in the three previous solar cycles. We observe certain peculiar features in cosmic ray modulation during the minimum of solar cycle 23 including the record high GCR intensity. We find, during this unusual minimum, that the correlation of GCR intensity is poor with sunspot number (correlation coefficient R=?0.41), better with interplanetary magnetic field (R=?0.66), still better with solar wind velocity (R=?0.80) and much better with the tilt angle of the heliospheric current sheet (R=?0.92). In our view, it is not the diffusion or the drift alone, but the solar wind convection that is the most likely additional effect responsible for the record high GCR intensity observed during the deep minimum of solar cycle 23.     

Solar Polarity Dependence of Cosmic Ray Power Spectra Observed with Mawson Underground Muon Telescopes

Power spectral density (PSD) of cosmic rays has been calculated from hourly averaged counts observed by underground muon telescopes located at Mawson over the low-frequency range 2.7×10⁻⁷ – 1.4×10⁻⁴ Hz. The first two harmonics of the solar daily variation are well defined for even cycles (20 and 22) whereas only the first harmonic is defined in cycle 21. The amplitude of the diurnal variation is lower for even cycles than for the odd cycle. The spectral power of the odd cycle exceeds those of the even cycles. The spectra are flatter and have lower power when the interplanetary magnetic field (IMF) is directed away from the Sun above the current sheet (A>0) than when the IMF is directed toward the Sun above the current sheet (A<0). The spectra imply that heliospheric magnetic turbulence may be more variable on time scales of several years than previously suspected.     

Description of Solar Cosmic Ray Propagation in the Interplanetary Medium on the Basis of the Kinetic Equation

The propagation of solar cosmic rays in interplanetary space is considered based on the kinetic equation. The expression for cosmic ray density under instantaneous particle injection by a point-like source is obtained. The set of a differential equation system for harmonics of cosmic ray distribution function is obtained starting from the kinetic equation. The cosmic ray transport equation, taking into account the presence of the second harmonic of particle angular distribution, is derived and the solution of this equation is obtained.     

Ineffectiveness of Narrow CMEs for Cosmic Ray Modulation

Monthly coronal mass ejection (CME) counts, – for all CMEs and CMEs with widths >?30^°, – and monthly averaged speeds for the events in these two groups were compared with both the monthly averaged cosmic ray intensity and the monthly sunspot number. The monthly P _i-index, which is a linear combination of monthly CME count rate and average speed, was also compared with the cosmic ray intensity and sunspot number. The main finding is that narrow CMEs, which were numerous during 2007?–?2009, are ineffective for modulation. A cross-correlation analysis, calculating both the Pearson (r) product–moment correlation coefficient and the Spearman (ρ) rank correlation coefficient, has been used. Between all CMEs and cosmic ray intensity we found correlation coefficients r=??0.49 and ρ=??0.46, while between CMEs with widths >?30^° and cosmic ray intensity we found r=??0.75 and ρ=??0.77, which implies a significant increase. Finally, the best expression for the P _i-index for the examined period was analyzed. The highly anticorrelated behavior among this CME index, the cosmic ray intensity (r=??0.84 and ρ=??0.83), and the sunspot number (r=+?0.82 and ρ=+?0.89) suggests that the first one is a very useful solar–heliospheric parameter for heliospheric and space weather models in general.